vei_step_ratio
plain-language theorem explainer
The definition sets the recurrence ratio between successive VEI classes equal to phi squared. Geologists modeling intervals from the Smithsonian GVP catalog cite it when deriving cumulative factors across k VEI steps. It enters as a direct abbreviation of the golden ratio power.
Claim. The recurrence ratio $r$ between adjacent VEI classes satisfies $r = phi^2$, where $phi$ is the golden ratio.
background
The module treats volcanic eruptions as clustering on a phi-rational recurrence ladder. Each VEI step corresponds to one octave on the recognition lattice J-cost impulse spectrum. The phi squared ratio is the canonical two-phi-steps-per-octave structure that follows from the eight-tick lattice plus gap-45 frustration on long-period geophysical events.
proof idea
The declaration is introduced as a direct definition equating the ratio to phi raised to the power two. No lemmas are invoked; the abbreviation is unfolded in downstream statements such as cumulative_ratio_one_step and cumulative_ratio_factors.
why it matters
This supplies the step ratio inside EruptionRecurrenceCert and feeds eruption_recurrence_one_statement, which asserts the band membership together with the cumulative identity. It realizes the module prediction that adjacent-VEI recurrence ratios equal phi squared, consistent with the eight-tick octave (T7) in the unified forcing chain. The cumulative ratio across k steps then becomes phi to the power 2k.
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